We typically assume the to correct way to solve a problem is to test for when the solution is true, not necessarily for when the solution is false. This is why I like the mythbusters montra "failure is always an option". Because in problem solving you can't reach a conclusion until you've both tested when a solution is true and when a solution is false. If you took the problem, how big is the Earth, you wouldn't be able to reach the correct conclusion until you knew where the earth is and where it isn't. This is also what your doctor does when you go to see him, he gathers a list of the signs and symptoms you have and immediately determines what isn't wrong with you, that leaves him with a list of possibilities about what could be wrong. It's not cost effective to test for each possible ailment individually, so tests are run that won't prove you have anything but will disprove multiple possibilities until you're left with only one possibility, which the doctor will declare is what you have.
That idea in problem solving is actually faster and more accurate, testing for what the solution isn't until you only have one or two options, then test for what the solution is.
